Split-plot Design

Hey
listers,

?



?

It’s good to know that I still
have a lot of search to do…

?

According to the two procedures AOV
and LME, I got two different results and I didn’t understand at all
the results of LME… There is a coefficient estimate of each level
and I just pretend to test if the effects of the factors and interaction
are significant or not…So I would like to learn more about this
function, because it's adequate for split-plot design...
test.anova=
aov(mes ~ nitro*thatch + Error(block/nitro), data=test)

?

summary(test.anova)

?

test.lme
<- lme(mes ~ nitro*thatch,random= ~ 1|block/nitro, data=test)

?

summary(test.lme)

?

Does anybody has any document or
reference that explain this results in details of the lme&hellip;
I&rsquo;ve looked for, but I didn&rsquo;t find any good
explication&hellip; I notice that there is a lot of information about the
lmer, but I am going step by step&hellip;

?



?

Thanks,

?



?

Ribeiro

?


?

Thanks for your response John. I just have one quick comment

about 

the Kenward-Roger degrees of freedom calculation. It has

been some 

time since I looked at that paper but my impression

at the time was 

that the equations would not easily translate

into the formulation 

used in lmer. The approach used in lmer is

like that of Henderson's 

mixed model equations (with many

modifications). That is, it is based 

on a penalized least

squares problem, not a generalized least squares 

problem. My

recollection is that Kenward and Roger wrote their 

equations in

terms of the generalized least squares problem. 

You

are not the first person to suggest that incorporating the 

Kenward-Roger calculation would enhance lmer. The reason I haven't 

done so is that I believe it is far from trivial to do so and I

have 

many, many other enhancements I would prefer to spend my

time on. 

However, this is open source software and any

enterprising person who 

wants to implement it is more than

welcome to do so. It may be 

sufficiently involved to be a

thesis topic - I don't know because I 

haven't studied it

carefully enough. 

Any person considering doing that

should read or reread Bill Venables' 

"Exegeses on Linear

Models" before embarking on it. As he points out 

in his

discussion of modifications made in S-PLUS to emulate some 

calculations in SAS, the "brute force" approach of taking a set
of 

equations and implementing them literally is rarely a good

approach. 

So I am not talking about a "pidgin R"

implementation here where a 

linear least squares calculation is

written 

XpX <- t(X) %*% X 
XpXinv <-

solve(XpX) 

Xpy <- t(X) %*% y 
betahat <- XpXinv

%*% Xpy 

An mer object includes slots L, RZX and RX

that define the Cholesky 

decomposition of the crossproduct

matrix that is more-or-less like 

that in the Henderson mixed

model equations. The L slot itself has a 

Perm slot that gives

the fill-reducing permutation P for the random 

effects. That

may not be relevant - I'm not sure. The original model 

matrices

are available as the X and Zt (transpose of Z) slots. The 

(transpose of the) derived model matrix for the orthogonal random 

effects is available as A. The terms attribute of the model matrix

X 

and the assign attribute of the model frame (in the slot

named 

"frame") should be used to associate terms with

columns of the model 

matrix. 

It's

possible that the calculation would be straightforward. As i 

said, I don't know. My gut feeling is that it is not, which is why I 

haven't embarked on it.